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<table width="100%" summary="page for Schmid"><tr><td>Schmid</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>12 variables created by Schmid and Leiman to show the Schmid-Leiman Transformation</h2>

<h3>Description</h3>

<p>John Schmid and John M. Leiman (1957) discuss how to transform a hierarchical factor structure to a bifactor structure. Schmid contains the example 12 x 12 correlation matrix. schmid.leiman is a 12 x 12 correlation matrix with communalities on the diagonal. This can be used to show the effect of correcting for attenuation. Two additional data sets are taken from Chen et al. (2006).
</p>


<h3>Usage</h3>

<pre>data(Schmid)</pre>


<h3>Details</h3>

<p> Two artificial correlation matrices from Schmid and Leiman (1957). One real and one artificial covariance matrices from Chen et al. (2006). 
</p>

<ul>
<li><p> Schmid: a 12 x 12 artificial correlation matrix created to show the Schmid-Leiman transformation. 
</p>
</li>
<li><p> schmid.leiman: A 12 x 12 matrix with communalities on the diagonal.  Treating this as a covariance matrix shows the 6 x 6 factor solution
</p>
</li>
<li><p> Chen: An 18 x 18 covariance matrix of health related quality of life items from Chen et al. (2006). Number of observations = 403.  The first item is a measure of the quality of life.  The remaining 17 items form four subfactors: The items are (a) Cognition subscale: &ldquo;Have difficulty reasoning
and solving problems?&quot;  &ldquo;React slowly to things that were said or done?&quot;; &ldquo;Become confused and start several actions at a time?&quot;  &ldquo;Forget where you
put things or appointments?&quot;; &ldquo;Have difficulty concentrating?&quot;  (b) Vitality
subscale: &ldquo;Feel tired?&quot;  &ldquo;Have enough energy to do the things you want?&quot; (R) 
&ldquo;Feel worn out?&quot; ; &ldquo;Feel full of pep?&quot; (R). (c) Mental health subscale: &ldquo;Feel
calm and peaceful?&quot;(R)  &ldquo;Feel downhearted and blue?&quot;; &ldquo;Feel very
happy&quot;(R) ; &ldquo;Feel very nervous?&quot; ; &ldquo;Feel so down in the dumps nothing could
cheer you up?  (d) Disease worry subscale: &ldquo;Were you afraid because of your health?&quot;; &ldquo;Were you frustrated about your health?&quot;; &ldquo;Was your health a worry in your life?&quot; .
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</li>
<li><p> West: A 16 x 16 artificial covariance matrix from Chen et al. (2006).
</p>
</li></ul>



<h3>Source</h3>

<p>John Schmid Jr. and John. M. Leiman (1957), The development of hierarchical factor solutions.Psychometrika, 22, 83-90.
</p>
<p>F.F. Chen, S.G. West, and K.H. Sousa.(2006) A comparison of bifactor and second-order models of quality of life. Multivariate Behavioral Research, 41(2):189-225, 2006.
</p>


<h3>References</h3>

<p>Y.-F. Yung, D.Thissen, and L.D. McLeod. (1999) On the relationship between the higher-order factor model and the hierarchical factor model. Psychometrika, 64(2):113-128, 1999.
</p>


<h3>Examples</h3>

<pre>
data(Schmid)
cor.plot(Schmid,TRUE)
print(fa(Schmid,6,rotate="oblimin"),cut=0)  #shows an oblique solution
round(cov2cor(schmid.leiman),2)
cor.plot(cov2cor(West),TRUE)
</pre>


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